When is the earliest time calculation for making kiddush when Asara b’Teves is on Friday?
We have to wait for nightfall before making kiddush, however we can daven maariv early to enable us to make kiddush right away (just we have to remember to say kriyas shema again). As far as the exact time that the fast ends, that you should look up in the local calendars. If you don’t have a calendar, let me know where you live, and I try to look it up for you.
O:CH 550-3, Aruch Hashulchan 550-2, Nitei Gavriel (Chanukah) 63-6.